Regards from Doctorspring.
Your symptoms are typical of bronchial asthma (late night and early morning cough, exercise induced cough, wheeze), and they are being precipitated by cold weather.
Having a past history of asthma, you are prone to have recurrent attacks of the same.
asthmatics may not feel symptoms always. even if they have mild - moderate symptoms, we usually ignore it to fatigue, exertion etc. only when it becomes moderate to severe do they consider as activity restricting asthma. Possibly the change in weather might have triggered asthma. You need to suppress the disease by a disease modifier.
Suggest a treatment plan for asthma - as it is causing symptoms i night, it is classified as "moderate persistant asthma".
The best approach would be a Steroid + Long acting beta agonist inhaler twice a day regularly, for 2- 3 weeks AFTER total symptom control. Once you are asymptomatic for 2- 3 weeks ( or after climate change), can taper down / stop the inhalers.
Hope this helped.please feel free to ask any clarifications if needed.
Dr. Jacob George P